PAST PAPER- 2019
Instructions:
• This paper is 30 minutes long.
• The maximum marks for this paper is 30.
Questions
1. Two cyclists start from the middle of a 200m track and move in opposite
directions towards the end of the track at 5m/s and 10m/s respectively. At the time
when a cyclist first reaches the end, both cyclists turn around and start moving
towards each other with their initial speeds. During this motion, a fly moves at a
speed of 17 m/s, between the 2 cyclists, landing on one cyclist and then moving to
the next continuously. How much distance has the fly covered when the two
cyclists meet again? (3 marks)
2. A square of side n meters contains n circles of radius 1m. If the probability of
hitting a circle is at least half, what is the minimum number of circles? (3 marks)
3. Two teams are playing a game. The format is best of 7 (first team to win four
games wins). Each game can only be won or lost, not tied. Is a team more likely to
win in 6 games, or 7? (4 marks)
4. An athlete takes a lap of a track with a speed v. At what speed must he cover the
second lap, so that his average speed for the 2 laps is 2v? (4 marks)
(A) v
(B) 2v
(C) 3v
(D) 1.5 v
5. If m, n and p are positive integers with 𝑚 +
(A) 3
(B) 4
(C) 1
(D) 17
!
!
!!!
=
(E) None of these
!"
!
, the value of n is:
(E) 13
(3 marks)
6. Equilateral triangle ABC has side length 3, with
vertices B and C on a circle of radius 3 as shown. The
triangle is then rotated clockwise inside the circle:
first about C until A reaches the circle, and then about
A until B reaches the circles, and so on. Eventually the triangle returns to its
original positions and stops. What is the total distance travelled by the point B? (5
marks)
7. A group of dragons and sheep are randomly divided into 2 equal rows. Each
animal in one row is directly opposite an animal in the other row. If 75 of the
animals are dragons, and the number of sheep opposite sheep is 10 more than the
number of dragons, find the total number of animals in the group. (4 marks)
8. If 200 is added to a positive integer I, the result is a square number. If 276 is added
to the same integer I, another square number is obtained. Find I. (4 marks)