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13.
A biscuit company makes cream biscuits that have 5 cm diameter and 0.5 cm thickness. It markets these biscuits in cylindrical packets of 5, 10, and 20 pieces each. The gaps between biscuits as well as between the packing and the biscuits are negligible. The ends of each packet are sealed with cardboard caps that have the company's logo printed on them. In your calculations, use pie = 22/7.
[1] The total surface areas of the above three types of packets will have the following proportion:
(1) 1 : 2 : 2.5
(2) 1 : 2 : 3
(3) 1 : 1.5 : 2
(4) 1 : 1.5 : 2.5[2] The Company buys printed packing sheets made of paper each having 100 × 66 cm2 area. At full capacity, the company makes 3.5 lakhs biscuits per day. If it makes 10,000 packets each of the 5's, 10's and 20's, what is the minimum number of packing sheets required daily?
(1) 417
(2) 419
(3) 420
(4) 418
[3] The cost of each biscuit is Rs. 0.40, each packing sheet is Rs. 168, and that of each end-cap is Rs. 0.50. All other costs work out to Rs. 1 per packet, irrespective of the size of the packet. The maximum retail price of the 5's, 10's and 20's Packets are Rs. 8, 14, and 23 respectively. The profits per packet P5, P10 and P20, made by the company on the 5's, 10's and 20's packets respectively will be in the proportion:
(1) 1 : 2 : 3
(2) 1 : 1.5 : 2.5
(3) 1 : 1.75 : 2.875
(4) 1 : 2 : 4[4] Based on a study of its sales over the last three years, the company decides to produce only 5000 packets of 20's. The production capacity thus made available is used to produce additional 5's and 10's packets to meet the market demand. Let x1 and x2 respectively represent the additional numbers of 5's packets (in thousands), and 10's packets (in thousands). For every thousand of the additional 5's packets, the company has 15 distributors, and for every thousand of the additional 10's packets, it has 5 distributors. The company can utilize the services of a maximum of 75 distributors for these additional packets. Then the product-mix problem for producing the additional packets of 5's and 10's (in thousands) can be modelled using a Linear Programming Formulation. Which of the following statements about this model is incorrect?
(1) Maximize P5 × x1 + P10 × x2 can be the objective function
(2) 15x1 + 5x2 ≤ 75 is a constraint
(3) 5x1 + 10x2 = 100 is a constraint
(4) x1 and x2 ≥ 0, and integers[5] How many additional thousand packets of 5's and 10’s should the company produce to maximize its profits?
(1) x1 = 3; x2 = 7
(2) x1 = 2; x2 = 10
(3) x1 = 2; x2 = 9
(4) solution is infeasible[6] The 5’s, 10's and 20's biscuit packets are produced in lot sizes of 100 each. Three packets each of 5's, 10's and 20's are inspected at random. If even one biscuit is found broken in any of the three, the respective lot is rejected, the probability that 1 broken biscuit will be found in a 5's, 10's or 20's packet is estimated to be 0.10, 0.20 and 0.30 respectively. If a sample of three packets each of 5's, 10's and 20's is inspected, which probability distribution should we use to estimate the probability that all nine packets will be accepted?
(1) Normal (2) Binomial (3) Poisson (4) Hyper geometric
[7] What is the probability that all nine packets will be accepted'?
(1) 0.749 (2) 0.006 (3) 0.128 (4) 0.504asked in JMET
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14.
A retail major has a warehouse (W) located at (16, 10) in a town having roads laid on a square grid parallel to the x and y axes. There are five retail supermarkets (M, N, O, P and Q) located respectively at (4, 4), (6, 16), (16, 24), (20, 16) and (26, 4).
[1] What is the ordering of the supermarkets from the nearest to the farthest from the warehouse?
(1) P, M, N and Q, O
(2) P, N and Q, O, M
(3) P, O, N and Q, M
(4) P, O, M, N and Q[2] Suppose each square block in the grid has sides of length 2 km. The minimum length of a round trip starting from M and moving through N, O, P, Q and returning to M will be
(1) 84 km
(2) 42 km
(3) 80 km
(4) None of these[3] Five trucks are used, one each to travel from the warehouse to the supermarkets M, N, O, P and Q. Suppose their average speeds are respectively 54, 50, 42, 25 and 40 km/hr. Assume that the trucks are identical and their drivers have identical driving skills and styles. If five trucks start simultaneously from the warehouse, which truck will reach its destination the earliest?
(1) W to M
(2) W to O
(3) W to P
(4) W to Nasked in JMET
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15.
Three BPOs, X, Y and Z have 500, 650 and 800 permanent employees respectively on 1st January 2006. The table below provides data on the average number of employees who quit one BPO and join another in a month.
TO ->
From (↓)X Y Z X 0 5 3 Y 8 0 1 Z 10 12 0
The second table below provides data on the retirements and retrenchments from X, Y und Z (these people are not re-employed in any of these three companies), and the additional fresh recruitments made by the three BPOs per month.X Y Z Retirements and
Retrenchments3 6 10 Fresh Recruits 10 12 20
All the joining or leaving events happen at the end of each month.[1] What will be the employee strengths of the three companies on 31st December 2006?
(1) X = 704; Y = 818; Z = 704
(2) X = 687; Y = 804; Z = 712
(3) X = 610; Y = 738; Z = 602
(4) X = 620; Y = 746; Z = 584[2] In which month will, the sum of the absolute value of differences in employee strengths between X and Y, and Y and Z be least?
(1) June
(2) July
(3) August
(4) Septemberasked in JMET
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16.
Three companies, Muck-In-Sea (MIS), Cold Man's Axe (CMA), and Bark Laze Bank (BLB) are scheduled, in that order, to interview 8 young MBA wizards at Hogwarts for offering Career placements on Day minus 13/8. Each company can select at most 3 students. Once a student receives an offer from a company, that student is not allowed to appear in any more interviews.
[1] How many possible combinations of student selections are there for MIS?
(1) 4
( 2) 93
(3) 92
(4) 3[2] What is the probability that CMA also does not select any student if MIS does not select any student?
(1) 1/4
(2) 1/3
(3) 1/92
(4) 1/93[3] Considering all the options (0, 1, 2 or 3 students) exercised by MIS and CMA, how many options does BLB have to make its selection?
(1) 3
(2) 4
(3) 63
(4) None of theseasked in JMET
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17.
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18.