CAT 2006 Question Paper

Instructions

A punching machine is used to punch a circular hole of diameter two Units from a square sheet of aluminium of width 2 units, as shown below. The hole is punched such that the circular hole touches one corner P of the square sheet and the diameter of the hole originating at P is in line with a diagonal of the square:

CAT 2006 - Question 1


The proportion of the sheet area that remains after punching is:

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CAT 2006 - Question 2


Find the area of the part of the circle (round punch) falling outside the square sheet.

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Instructions

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and Praja have 60 kg of luggage between them, and are charged Rs 1200 and Rs 2400 respectively for excess luggage. Had the entire luggage belonged to one of them, the excess luggage charge would have been Rs 5400.

CAT 2006 - Question 3


What is the weight of Praja’s luggage?

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CAT 2006 - Question 4


What is the free luggage allowance?

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Instructions

For the following questions answer them individually

CAT 2006 - Question 5


If x = -0.5, then which of the following has the smallest value?

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CAT 2006 - Question 6


Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?

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CAT 2006 - Question 7


If a/b = 1/3, b/c = 2, c/d = 1/2 , d/e = 3 and e/f = 1/4, then what is the value of abc/def ?

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CAT 2006 - Question 8


The length, breadth and height of a room are in the ratio 3:2:1. If the breadth and height are halved while the length is doubled, then the total area of the four walls of the room will

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CAT 2006 - Question 9


Consider a sequence where the $$n^{th}$$ term, $$t_n = n/(n+2), n =1, 2, ....$$ The value of $$t_3 * t_4 * t_5 * …..* t_{53}$$ equals.

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CAT 2006 - Question 10


A group of 630 children is arranged in rows for a group photograph session. Each row contains three fewer children than the row in front of it. What number of rows is not possible?

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