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295.

If D is the midpoint of side BC of a triangle ABC and AD is the perpendicular to AC then:
A. 3AC² = BC² – AB²
B. 3BC² = AC² – 3AB²
C. BC² + AC² = 5AB²
D. None of the above

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While packing for a business trip Mr. Debashis has packed 3 pairs of shoes, 4 pants, 3 half-pants, 6 shirts, 3 sweater and 2 jackets. The outfit is defined as consisting of a pair of shoes, a choice of "lower wear" (either a pant or a half-pant), a choice of "upper wear" (it could be a shirt or a sweater or both) and finally he may or may not choose to wear a jacket. How many different outfits are possible?
A. 567
B. 1821
C. 743
D. None of the above

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McDonald‘s ran a campaign in which it gave game cards to its customers. These game cards made it possible for customers to win hamburgers, French fries, soft drinks, and other fast-food items, as well as cash prizes. Each card had 10 covered spots that could be uncovered by rubbing them with a coin. Beneath three of these spots were "No Prize" signs. Beneath the other seven spots were names of the prizes, two of which were identical. For, example, one card might have two pictures of a hamburger, one picture of a coke, one of French fries, one of a milk shake, one of a $5, one of $1000, and three "No Prize" signs. For this card the customer could win a hamburger. To win on any card, the customer had to uncover the two matching spots (which showed the potential prize for that card) before uncovering a "No Prize" any card with a "No Prize" uncovered was automatically void. Assuming that the two matches and the three "No Prize" signs were arranged randomly on the cards, what is the probability of a customer winning?
A. 0.10
B. 0.15
C. 0.12
D. None of the above

asked in IIFT

Answer the questions based on the following information.
Rajat is sales manager of Dubin Computers Ltd. and looks after Delhi market. The company sells laptops in India. He is currently trying to select a distributor for coming five years. The distributor ensures that the products are accessible to the customers in the market. Market share of a company depends on the coverage by the distributor.
The total profit potential of the entire laptop market in Delhi is Rs. 5 crores in the current year and present value of next four years‘ cumulative profit potential is Rs. 15 crores.
The first choice for Rajat is to enter into long-term contract with a distributor M/s Jagan with whom Dubin has done business in the past, and whose distribution system reaches 55 percent of all potential customers. At the last moment, however, a colleague suggests Rajat to consider signing a one-year contract with other distributors. Distributors M/s Bola and M/s James are willing to be partner with Dubin. Although a year ago M/s Bola‘s and M/s James‘s coverage reached only 40 and 25 percent of customers respectively, they claim to have invested heavily in distribution resources and now expect to be able to reach 60 percent and 75 percent of customers respectively. The probability of M/s Bola‘s claim and M/s James‘s claim to be true is 0.60 and 0.20 respectively. The knowledge about distributors‘ coverage will evolve over time. The assumption is that the true level of coverage offered by the new distributors could be discovered, with certainty, through a one-year trail, and this trail will reveal exactly one of the two levels of coverage: for example in case of M/s Bola – 40 percent (as it was last year) or 60 percent (as claimed). In addition, it is also assumed that whatever the coverage is for both distributors, it will not change over time. Rajat narrows down on three choices, which are as follows:
Choice 1. Give a five year contract to the familiar distributor M/s Jagan
Choice 2. Give a one year contract to the new distributor M/s Bola, and base next year‘s decision to renew contract with M/s Bola on observed coverage for next four years contract with M/s Jagan.
Choice 3. Give a one-year contract to the new distributor M/s James, and base next year‘s decision to renew contract with M/s James on observed coverage for next four years contract with M/s Jagan.

[1]	The expected present value of the five years cumulative profit with choice 3 is: A. Rs. 12.7 crores B. Rs. 10.6 crores C. Rs. 11.7 crores D. None of the above

[2]	Which of the following statement is TRUE? A. Choice 1 is more profitable than Choice 2 B. Choice 3 is more profitable than Choice 2 C. Choice 3 is more profitable than Choice 1 D. None of the above

[3]

If the distributor M/s James claims a coverage of 55% instead of 75% and probability of this claim to be true is 0.70 instead of 0.20 then which of the following statement is true?
A. Choice 1 is more profitable than Choice 2
B. Choice 2 is more profitable than Choice 3
C. Choice 3 is more profitable than Choice 1
D. None of the above

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299.

The game of "chuck-a-luck" is played at carnivals in some parts of Europe. Its rules are as follows: if u pick a number from 1 to 6 and the operator rolls three dice. If the number you picked comes up on all three dice, the operator pays you ∈3; if it comes up on two dice, you are paid ∈2; and if it comes up on just one die, you are paid ∈1. Only if the number you picked does not come up at all, you pay the operator ∈1. The probability that you will win money playing in this game is:
A. 0.52
B. 0.753
C. 0.42
D. None of the above

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300.

A medical clinic tests blood for certain disease from which approximately one person in a hundred suffers. People come to the clinic in group of 50. The operator of the clinic wonders whether he can increase the efficiency of the testing procedure by conducting pooled tests. In the pooled tests, the operator would pool the 50 blood samples and test them altogether. If the polled test was negative, he could pronounce the whole group healthy. If not, he could then test each person‘s blood individually. The expected number of tests the operator will have to perform if he pools the blood samples are:
A. 47
B. 25
C. 21
D. None of the above

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