CAT 1990 Question Paper

Instructions

The pages of a book are numbered 0, 1, 2 . upto M, M>0. There are four categories of instructions that direct a person in positioning the book at a page. The instruction types and their meanings are :
1. OPEN : Position the book at page No. 1
2. CLOSE : Position the book at page No. 0
3. FORWARD, n :From the current page move forward by n pages; if, in this process, page number M is reached, stop at M.
4. BACKWARD, n : From the current page, move backward by n pages; if in this process, page number 0 is reached, stop at page number 0.
In each of the following questions, you will find a sequence of instructions formed from the above categories. In each case, let n1 be the page number before the instructions are executed and n2 be the page number at which the book is positioned after the instructions are executed.

Question 41

FORWARD, 25 ; BACKWARD, 10. which of the following statements is true?

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Question 42

BACKWARD, 5; FORWARD, 5. Which of the following statements is true about the above set of instructions?

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Question 43

FORWARD, 10; FORWARD, 10. Which of the following statements about the above instructions is true?

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Question 44

FORWARD, 5; BACKWARD, 4. Which of the following statements about the above instructions is true?

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Instructions

There are 5 cities, A, B, C, D and E connected by 7 roads as shown in the figure below:




Design a route such that you start from any city of your choice and walk on each of the 7 roads once and only once, not necessarily returning to the city from which you started.

Question 45

For a route that satisfies the above restrictions, which of the following statements is true?

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Question 46

How many different starting cities are possible such that the above restriction is satisfied?

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Instructions

For the following questions answer them individually

Question 47

If $$xy + yz + zx = 0$$, then $$(x + y + z)^2$$ equals

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Question 48

If equal numbers of people are born on each day, find the approximate percentage of the people whose birthday will fall on 29th February. If we are to consider people born in 20th century (1901-2000) and assuming no deaths.

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Question 49

I brought 30 books on Mathematics, Physics, and Chemistry, priced at Rs.17, Rs.19, and Rs.23 per book respectively, for distribution among poor students of Standard X of a school. The physics books were more in number than the Mathematics books but less than the Chemistry books, the difference being more than one. The total cost amounted to Rs.620. How many books on Mathematics, Physics, and Chemistry could have been bought respectively?

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Question 50

The last time Rahul bought Diwali cards, he found that the four types of cards that he liked were priced Rs.2.00, Rs.3.50, Rs.4.50 and Rs.5.00 each. As Rahul wanted 30 cards, he took five each of two kinds and ten each of the other two, putting down the exact number of 10 rupees notes on the counter payment. How many notes did Rahul give?

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