16-01-2013, 03:18 PM
CAT 2007 QUESTION
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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
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. What is the time difference between A and B?
(1) 1 hour and 30 minutes
(2) 2 hours
(3) 2 hours and 30 minutes
(4) 1 hour
(5) Cannot be determined
5. What is the plane’s cruising speed in km per hour?
(1) 700
(2) 550
(3) 600
(4) 500
(5) Cannot be determined
6. Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
(1) 3
(2) 2
(3) 4
(4) 0
(5) 1
7. In a tournament, there are n teams T1 , T2 ..., T with n > 5. Each team consists of k players, k > 3. The following pairs of teams have one player in common:
T1 & T2 , T2 & T3 ,.., Tn − 1 & Tn , and Tn & T1.