Q.1 Diameters of two circular coins are in the ratio of 1:3. The smaller coin is to roll around the bigger coin till it returns to the position from where the process of rolling started. How many times smaller coin rolled around the bigger coin ?
Since, Diameter of small coin/Diameter of big coin = 1/3
Radius of small coin/Radius of big coin = 1/3
Therefore, circumference of small coin = 2pk
Circumference of big coins = 2p (3 k)
= 6pk = 3 (2pk)
Q.2 A ray of light is incident towards a plane mirror at an angle of 60O with the mirror surface. What will be the value of angle of reflection ?
Since, Normal to the surface of mirror is 900,
Therefore angle of incidence will be 90 – 60 = 300
As angle of reflection must be equal to the angle of incidence according to the laws of reflection.
Q.3 A man is facing west turns through 450 clockwise, again 1800 clockwise and then turns through 2700 anti clockwise. Which direction is he facing now?
Clearly, the man initially faces in the west direction. On moving 45o clockwise, he faces in the direction North. On further moving 180o clockwise, he faces in the direction South. Finally, on moving 270o anti–clockwise, he faces in the direction, which is South–west.
Q.4 I am facing east. I turn 1000 in the clockwise direction and then 1450 in the anticlockwise direction. Which direction am I facing now?
Q.5 A bus starts from city A. The no. of women in the bus is half of the no. of men. In city B, 10 men left bus & 5 women entered. Now no. of men & women is equal. In the beginning how many passengers entered the bus?
Suppose in city A the no of men is 2x
Then the no. of women is =x
In city B: 2x-10 = x+5
So, A= 30
Thus , the no. of passengers in the beginning