Clock

A clock has 2 hands, the smaller one is called the hour hand or short hand while the larger one is called the minute hand or long hand.
The face of a clock is a circle which subtends an angle of 360° at the centre.

Some Important Points

In every hour
1.

• Both the hands coincide once. At this point the angle between them is 0°.
• The hands are straight (point in opposite directions) once. At this point the angles between them are 180°.
• The hands are twice perpendicular to each other. At this point the angle between them is 90°.

2.

• In 60 min the minute hand covers 360°.
  Thus, in 1 min the minute hand covers (360/60)° = 6°
• In 12 h the hour hand covers 360°.
  Thus, in 1 min the hour hand covers (360/(12 x 60)) = 1°/2
  Thus, in 1 minute, the minute hand gains (6 - 1/2)° = 11°/2, than the hour hand.

3.

• When the two hands are at right angles, they are 15min spaces apart.
• When the two hands are in opposite directions, they are 30 min spaces apart.
• In 60 min the minute hand gains 55 min on the hour hand.
• The minute hand moves 12 times as fast as the hour hand.

4.

• Too Fast: If a clock indicates 7 : 1.5, when the correct time is 7, it is said to be 15 min too fast.
• Too Slow: If a clock indicates 7 : 30, when the correct time is 7 : 45 , it is said to be 15 min too slow.

Calendar

1. Odd Days: The number of days more than the complete weeks for a given period called odd days.
2. Ordinary Year: An ordinary year has 365 days and an ordinary year is not a leap year.
3. Leap Year:

• Any year (except a century) which is divisible by 4 is a leap year.
• However, every 4th century is a leap year, ie, a century is a leap year when it is divisible by 400.
• A leap year has 366 days.
  Examples of Leap Year 1924, 1908, 1944, 2008, 1684, etc., are all leap years.
  400, 800, 1200, 1600, 2000, etc., are all leap years.

4. Counting of Odd Days
(1) 1 ordinary year = 365 days = (52 weeks + 1 day) Þ 1 ordinary year = 1 odd day
(2) 1 leap year = 366 days = (52 weeks + 2 days) = 1 leap year = 2 odd days
(3) 100 yr = 76 ordinary years + 24 leap years = (76 × 1 + 24 × 2) odd days = 124 odd days
= (17 weeks + 5 days) = 5 odd days
(4) 200 yr = (5 × 2) = 10 odd days = (1 week + 3 days) = 3 odd day
(e) 300 yr = (5 × 3) = 15 odd days = (2 weeks + 1 day) = 1 odd days
(f) 400 yr = (5 × 4 + 1) = 21 odd days = (3 weeks + 0 day) = 0 odd day Similarly, 800 yr, 1200 yr, 1600 yr, 2000 yr have 0 odd days.