CAT 2001 Question Paper


For the following questions answer them individually

Question 41

Let x and y be two positive numbers such that $$x + y = 1.$$

Then the minimum value of $$(x+\frac{1}{x})^2+(y+\frac{1}{y})^2$$ is

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Question 42

Based on the figure below, what is the value of x, if y = 10?

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Question 43

A rectangular pool of 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 $$m^2$$ , how wide, in metres, is the walkway?

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Question 44

Let $$b$$ be a positive integer and $$a = b^2 - b$$. If $$b \geq 4$$ , then $$a^2 - 2a$$ is divisible by

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Question 45

Ashish is given Rs. 158 in one-rupee denominations. He has been asked to allocate them into a number of bags such that any amount required between Re 1 and Rs. 158 can be given by handing out a certain number of bags without opening them. What is the minimum number of bags required?

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Question 46

In some code, letters a, b, c, d and e represent numbers 2, 4, 5, 6 and 10. We just do not know which letter represents which number. Consider the following relationships:

I. a + c = e,
II. b - d = d and
III. e + a = b

Which of the following statements is true?

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Question 47

Ujakar and Keshab attempted to solve a quadratic equation. Ujakar made a mistake in writing down the constant term. He ended up with the roots (4, 3). Keshab made a mistake in writing down the coefficient of x. He got the roots as (3, 2). What will be the exact roots of the original quadratic equation?

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Question 48

A change-making machine contains one-rupee, two-rupee and five-rupee coins. The total number of coins is 300. The amount is Rs. 960. If the numbers of one-rupee coins and two-rupee coins are interchanged, the value comes down by Rs. 40. The total number of five-rupee coins is

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Question 49

The figure below shows the network connecting cities A, B, C, D, E and F. The arrows indicate permissible direction of travel. What is the number of distinct paths from A to F?

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Question 50

Let n be the number of different five-digit numbers, divisible by 4 with the digits 1, 2, 3, 4, 5 and 6, no digit being repeated in the numbers. What is the value of n?

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