CAT2000 Related Question Answers
101. The, sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the four given choices to construct a coherent paragraph.A.If caught in the act, they were punished, not for the crime, but for allowing themselves to be caught.B.The bellicose Spartans sacrificed all the finer things in life for military expertise.C.Those fortunate enough to survive babyhood were taken away from their mothers at the age of seven to undergo rigorous military training.D.This consisted mainly of beatings and deprivations of all kinds like going around barefoot in winter, and worse, starvation so that they would be forced to steal food to survive.E.Male children were examined at birth by the city council and those deemed too weak to become soldiers were left to die of exposure.
102.
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 BThe sum of A and B is given by:
104.
Directions for the next 2 questions:For real numbers x, y, letf(x, y) = Positive square-root of (x + y), if $$(x + y)^{0.5}$$ is real
f(x, y) = $$(x + y)^2$$; otherwiseg(x, y) = $$(x + y)^2$$, if $$\sqrt{(x + y)}$$ is real
g(x, y) = $$- (x + y)$$ otherwiseWhich of the following expressions yields a positive value for every pair of non-zero real numbers (x, y)?
106.
Directions for the next 3 questions: For three distinct real positive numbers x, y and z, letf(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)Which of the following is necessarily greater than 1?
109.
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.
110. 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?
111.
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
114. After executing a sequence of three instructions, bottle A contains one litre of water. The first and the third of these instructions are shown below: First instruction: FILL (C, A) Third instruction: FILL (C, A) Then which of the following statements about the instruction is true?
115. Consider the same sequence of three instructions ‘and the same initial state mentioned above. Three more instructions are added at the end of the above sequence to have A contain 4 litres of water. In this total sequence of six instructions, the fourth one is DRAIN (A). This is the only DRAIN instruction in the entire sequence. At the end of the execution of the above sequence, how much water (in litres) is contained in C?
116.
Directions for the next 2 questions:For a real number x, let$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative
$$f(x) = 1+x,$$ if $$x$$ is negative$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$What is the value of the product, $$f(2) f^2(2)f^3(2) f^4(2)f^5(2)$$?
117.
Directions for the next 2 questions:For a real number x, let$$f(x) = 1/(1+x),$$ if $$x$$ is non-negative
$$f(x) = 1+x,$$ if $$x$$ is negative$$f^n(x) = f(f^{n-1}(x)), n = 2, 3.....$$r is an integer 2. Then, what is the value of $$f^{r-1}(-r) + f^r(-r) + f^{r+1}(-r)$$?
118. Let D be recurring decimal of the form, $$D = 0.a_1a_2a_1a_2a_1a_2...$$, where digits $$a_1$$ and $$a_2$$ lie between 0 and 9. Further, at most one of them is zero. Then which of the following numbers necessarily produces an integer, when multiplied by D?
119. 
In the above table, for suitably chosen constants a, b and c, which one of the following best describes the relation between y and x?
121. What is the value of the following expression?$$(1/(2^2-1))+(1/(4^2-1))+(1/(6^2-1))+...+(1/(20^2-1)$$
122. A truck travelling at 70 kilometres per hour uses 30% more diesel to travel a certain distance than it does when it travels at the speed of 50 kilometres per hour. If the truck can travel 19.5 kilometres on a litre of diesel at 50 kilometres per hour, how far can the truck travel on 10 litres of diesel at a speed of 70 kilometres per hour?[CAT 2000]
123. Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:[CAT 2000]
125. One red flag, three white flags and two blue flags are arranged in a line such that,A. no two adjacent flags are of the same colourB. the flags at the two ends of the line are of different colours.In how many different ways can the flags be arranged?
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