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IIM MBA Entrance Exam : Common Admission Test Question Paper CAT 2007

30 pages, 75 questions, 8 questions with responses, 8 total responses,

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CAT 2007 Section I This section contains 25 questions 1. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal? (1) May 21 (2) April 11 (3) May 20 (4) April 10 (5) June 30 2. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10? (1) 119 (2) 159 (3) 110 (4) -180 (5) -105 3. Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees? (1) Between 0 and 90 (2) Between 0 and 30 (3) Between 0 and 60 (4) Between 0 and 75 (5) Between 0 and 45 Directions for Questions 4 and 5: Let S be the set of all pairs (i, j) where 1 i j < n and n 4. Any two distinct members of S are called friends if they have one constituent of the pairs in common and enemies otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies. 4. For general n, how many enemies will each member of S have? (1) n 3 (2) (3) 2n 7 Page 1 of 30

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