XAT 2013 Question Paper

Instructions

For the following questions answer them individually

Question 71

Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the journey in Ram's car at the rate of 25 kmph, while Shyam walked at 5 kmph. After sometime, Hari got off and started walking at the rate of 5kmph and Ram went back to pick up Shyam. All three reached the destination simultaneously. The number of hours required for the trip was:

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Question 72

The central park of the city is 40 metres long and 30 metres wide. The mayor wants to construct two roads of equal width in the park such that the roads intersect each other at right angles and the center of the rectangle co-incides with the center of the rectangle formed by the intersection of the two roads . Further, the mayor wants that the area of the two roads to be equal to the remaining area of the park. What should be the width of the roads?

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Question 73

Arun has to go to the country of Ten to work on a series of tasks for which he must get a permit from the Government of Ten. Once the permit is issued, Arun can enter the country within ten days of the date of issuance of the permit. Once Arun enters Ten, he can stay for a maximum of ten days. Each of the tasks has a priority, and takes a certain number of days to complete. Arun cannot work on more than one task at a time. The following table gives the details of the priority and the number of days required for each task.


Arun's first priority is to complete as many tasks as possible, and then try to complete the higher priority tasks. His last priority is to go back as soon as possible.

The tasks that Arun should try to complete are:

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Question 74

Arun has to go to the country of Ten to work on a series of tasks for which he must get a permit from the Government of Ten. Once the permit is issued, Arun can enter the country within ten days of the date of issuance of the permit. Once Arun enters Ten, he can stay for a maximum of ten days. Each of the tasks has a priority, and takes a certain number of days to complete. Arun cannot work on more than one task at a time.

However, Arun's manager has told him to do some background research on the tasks before leaving for Ten. At the same time, there is no guarantee that the Government of Ten will give the permit to Arun. Background research involves substantial costs, and therefore Arun has decided that he will not start his background research without getting the permit.

The following table gives the details of the priority, the number of days required for each task and the number of days required for background research on each task.


Arun's first priority is to complete as many tasks as possible, and then try to complete the higher priority tasks. His last priority is to go back as soon as possible within ten days.

The tasks that Arun should try to complete are:

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Question 75

The radius of a circle with centre O is $$\sqrt{50}$$cm. A and C are two points on the circle, and B is a point inside the circle. The length of AB is 6 cm, and the length of BC is 2 cm. The angle ABC is a right angle. Find the square of the distance OB.

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Question 76

Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one of the cards drawn is a king, and b denote the probability of not drawing a king. The ratio a/b is

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Question 77

In the country of Four, there are four cities, A, B, C and D. B is to the East of A, C is to the South of B, D is to the West of C, and A is to the North of D. The Government of Four is planning to connect these four cities by road such that it is possible for a person to go from a city to any of the other three cities. At the same time, the Government wants to ensure that the total road length is minimum. The distances between A to B, B to C, C to D and D to A are all equal to 10 km. What should be the total length of the road?

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Question 78

Consider the expression $$(xxx)_{b}=x^3$$, where b is the base, and x is any digit of base b. Find the value of b:

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Question 79

Consider a function $$f(x) = x^4 + x^3 + x^2 + x + 1$$, where x is a positive integer greater than 1. What will be the remainder if $$f(x^5)$$ is divided by f(x)?

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Question 80

Please read the following sentences carefully:
I ā€” 103 and 7 are the only prime factors of 1000027
II ā€” $$\sqrt[6]{6!}>\sqrt[7]{7!}$$
III ā€” If I travel one half of my journey at an average speed of x km/h, it will be impossible for me to attain an average speed of 2x km/h for the entire journey.

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