# CMC-Past-Paper-2019

```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
!&quot;
!
, 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: