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103.

For which value of k does the following pair of equations yield a unique solution for x such that the solution is positive?
x² – y² = 0
(x – k)² + y² = 1
(1) 2
(2) 0
(3) √2
(4) -√2

asked in CAT

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104.

What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of radius 20 cm?
(1) 1 or 7
(2) 2 or 14
(3) 3 or 21
(4) 4 or 28

asked in CAT

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105.

If R = (30⁶⁵ - 29⁶⁵)/(30⁶⁴ + 29⁶⁴ ), then
(1) 0 < R ≤0.1
(2) 0.1 < R ≤ 0.5
(3) 0.5 < R ≤ 1.0
(4) R > 1.0

asked in CAT

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106.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at a speed of 10 km/hr, reaches B and comes back to A at the same speed.

[1] At what time do Ram and Shyam first meet each other?
(1) 10:00 a.m.
(2) 10:10 a.m.
(3) 10:20 a.m.
(4) 10:30 a.m.
[2] At what time does Shyam overtake Ram?
(1) 10:20 a.m.
(2) 10:30 a.m.
(3) 10:40 a.m.
(4) 10:50 a.m.

asked in CAT

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107.

In a chess competition involving some boys and girls of a school, every student had to play exactly one game with every other student. It was found that in 45 games both the players were girls, and in 190 games both were boys. The number of games in which one player was a boy and the other was a girl is
(1) 200
(2) 216
(3) 235
(4) 256

asked in CAT

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108.

A jogging park has two identical circular tracks touching each other, and a rectangular track enclosing the two circles. The edges of the rectangles are tangential to the circles. Two friends, A and B, start jogging simultaneously from the point where one of the circular tracks touches the smaller side of the rectangular track. A jog along the rectangular track, while B jogs along the two circular tracks in a figure of eight. Approximately, how much faster than A does B have to run, so that they take the same time to return to their starting point?
(1) 3.88%
(2) 4.22%
(3) 4.44%
(4) 4.72%

asked in CAT

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