CAT 2000 Question Paper
Directions for the next 2 questions:
A, B, C are three numbers.
Let @(A, B) = average of A and B,
/(A, B) = product of A and B, and
X(A, B) = the result of dividing A by B
Directions for the next 2 questions:
For real numbers x, y, let
f(x, y) = Positive square-root of (x + y), if $$(x + y)^{0.5}$$ is real
f(x, y) = $$(x + y)^2$$; otherwise
g(x, y) = $$(x + y)^2$$, if $$\sqrt{(x + y)}$$ is real
g(x, y) = $$- (x + y)$$ otherwise
Which of the following expressions yields a positive value for every pair of non-zero real numbers (x, y)?
Directions for the next 3 questions: For three distinct real positive numbers x, y and z, let
f(x, y, z) = min (max(x, y), max (y, z), max (z, x))
g(x, y, z) = max (min(x, y), min (y, z), min (z, x))
h(x, y, z) = max (max(x, y), max(y, z), max (z, x))
j(x, y, z) = min (min (x, y), min(y, z), min (z, x))
m(x, y, z) = max (x, y, z)
n(x, y, z) = min (x, y, z)
Directions for the next 2 questions: There are five machines A, B, C, D, and E situated on a straight line at distances of 10 metres, 20 metres, 30 metres, 40 metres and 50 meters respectively from the origin of the line. A robot is stationed at the origin of the line. The robot serves the machines with raw material whenever a machine becomes idle. All the raw material is located at the origin. The robot is in an idle state at the origin at the beginning of a day. As soon as one or more machines become idle, they send messages to the robot- station and the robot starts and serves all the machines from which it received messages. If a message is received at the station while the robot is away from it, the robot takes notice of the message only when it returns to the station. While moving, it serves the machines in the sequence in which they are encountered, and then returns to the origin. If any messages are pending at the station when it returns, it repeats the process again. Otherwise, it remains idle at the origin till the next message (s) is received.
Suppose on a certain day, machines A and D have sent the first two messages to the origin at the beginning of the first second, and C has sent a message at the beginning of the 5th second and B at the beginning of the 6th second, and E at the beginning of the 10th second. How much distance in metres has the robot travelled since the beginning of the day, when it notices the message of E? Assume that the speed of movement of the robot is 10 metres per second.
Suppose there is a second station with raw material for the robot at the other extreme of the line which is 60 metres from the origin, that. is, 10 meters from E. After finishing the services in a trip, the robot returns to the nearest station. If both stations are equidistant, it chooses the origin as the station to return to. Assuming that both stations receive the messages sent by the machines and that all the other data remains the same, what would be the answer to the above question?
Directions for the next 3 questions:
Given below are three graphs made up of straight-line segments shown as thick lines. In each case choose the answer as:
a) if f(x)=3f(-x)
b) if f(x)= -f(-x)
c) if f(x) = f(-x)
d) if 3f(x) = 6f(-x), for x >= 0
