CAT 2000

Instructions

For the following questions answer them individually

Question 141

Each of the numbers $$x_1, x_2, ... ,x_n$$ $$(n > 4)$$, is equal to 1 or -1.
Suppose, $$x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + ....... + x_{n-3}x_{n-2} x_{n-1}x_n x_1 + x_{n-1} x_n x_1 x_2 + x_n x_1 x_2x_3$$ = 0, then:

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Question 142

The table below shows the age-wise distribution of the population of Reposia. The number of people aged below 35 years is 400 million.

If the ratio of females to males in the ‘below 15 years’ age group is 0.96, then what is the number of females (in millions) in that age group?

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Question 143

Sam has forgotten his friend’s seven-digit telephone number. He remembers the following: the first three digits are either 635 or 674, the number is odd, and the number nine appears once. If Sam were to use a trial and error process to reach his friend, what is the minimum number of trials he has to make before he can be certain to succeed?

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Question 144

Let N = $$55^3 + 17^3 - 72^3$$. N is divisible by:

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Question 145

If $$x^2 + y^2 = 0.1$$ and |x-y|=0.2, then |x|+|y| is equal to:

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Question 146

ABCD is a rhombus with the diagonals AC and BD intersection at the origin on the x-y plane. The equation of the straight line AD is x + y = 1. What is the equation of BC?

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Question 147

Consider a circle with unit radius. There are 7 adjacent sectors, S1, S2, S3,....., S7 in the circle such that their total area is (1/8)th of the area of the circle. Further, the area of the $$j^{th}$$ sector is twice that of the $$(j-1)^{th}$$ sector, for j=2, ...... 7. What is the angle, in radians, subtended by the arc of S1 at the centre of the circle?

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Question 148

There is a vertical stack of books marked 1, 2 and 3 on Table-A, with 1 at the bottom and 3 on top. These are to be placed vertically on Table-B with 1 at the bottom and 2 on the top, by making a series of moves from one table to the other. During a move, the topmost book, or the topmost two books, or all the three, can be moved from one of the tables to the other. If there are any books on the other table, the stack being transferred should be placed, on top of the existing books, without changing the order of books in the stack that is being moved in that move. If there are no books on the other table, the stack is simply placed on the other table without disturbing the order of books in it. What is the minimum number of moves in which the above task can be accomplished?

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Question 149

The area bounded by the three curves |x+y| = 1, |x| = 1, and |y| = 1, is equal to:

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Question 150

If the equation $$x^3 - ax^2 + bx - a = 0$$ has three real roots, then it must be the case that,

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