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13.

From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Then they will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would be the contender numbered 2.

[1]	Which position should a contender choose if he has to be the leader? (5 marks) (1) 3 (2) 67 (3) 195 (4) 323 (5) 451

[2]

One of the contending politicians, Mr. Chanaya, was quite proficient in calculations and could correctly figure out the exact position. He was the last person remaining in the circle. Sensing foul play the politicians decided to repeat the game. However, this time, instead of removing every alternate person, they agreed on removing every 300th person from the circle. All other rules were kept intact. Mr. Chanaya did some quick calculations and found that for a group of 542 people the right position to become a leader would be 437. What is the right position for the whole group of 545 as per the modified rule?
(5 marks)

(1) 3
(2) 194
(3) 249
(4) 437
(5) 543

asked in XAT

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14.

In a city, there is a circular park. There are four points of entry into the park, namely - P, Q, R and S. Three paths were constructed which connected the points PQ, RS, and PS. The length of the path PQ is 10 units, and the length of the path RS is 7 units. Later, the municipal corporation extended the paths PQ and RS past Q and R respectively, and they meet at a point T on the main road outside the park. The path from Q to T measures 8 units, and it was found that the angle PTS is 60° . Find the area (in square units) enclosed by the paths PT, TS, and PS. (2 marks)
(1) 36√3
(2) 54√3
(3) 72√3
(4) 90√3
(5) None of the above

asked in XAT

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15.

The football league of a certain country is played according to the following rules:

-> Each team plays exactly one game against each of the other teams.
-> The winning team of each game is awarded l point and the losing team gets 0 point.
-> If a-match ends in a draw, both the teams get 1/2 point.

After the league was over, the teams were ranked according to the points that they earned at the end of the tournament. Analysis of the points table revealed the following:

-> Exactly half of the points earned by each team were earned in games against the ten teams which finished at the bottom of the table.
-> Each of the bottom ten teams earned half of their total points against the other nine teams in the bottom ten.

How many teams participated in the league?(3 marks)

(1) 16
(2) 18
(3) 19
(4) 25
(5) 30

last reply by CpjJwWHV • 10 years ago • asked in XAT

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16.

There are four machines in a factory. At exactly 8 pm, when the mechanic is about to leave the factory, he is informed that two of the four machines are not working properly. The mechanic is in a hurry, and decides that he will identify the two faulty machines before going home, and repair them next morning. It takes him twenty minutes to walk to the bus stop. The last bus leaves at 8:32 pm. If it takes six minutes to identify whether a machine is defective or not, and if he decides to check the machines at random, what is the probability that the mechanic will be able to catch the last bus? (2 marks)
(1) 0
(2) 1/6
(3) 1/4
(4) 1/3
(5) 1

last reply by CpjJwWHV • 14 years ago • asked in XAT

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17.

The domain of the function
f(x) = log₇ { log₃ (log₅ (20x – x² – 91 ))} is: (3 marks)
(1) (7, 13)
(2) (8, 12)
(3) (7, 12)
(4) (12, 13)
(5) None of the above

asked in XAT

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18.

A 25 ft long ladder is placed against the wall with its base 7 ft from the wall. The base of the ladder is drawn out so that the top comes down by half the distance that the base is drawn out. This distance is in the range: (2 marks)
(1) (2, 7)
(2) (5, 8)
(3) (9, 10)
(4) (3, 7)
(5) None of the above.

asked in XAT

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