**Theory:**

We all know, a clock is a device that measures and shows time. It has two arms. The longer arm is *minute hand* and the shorter arm is *hour hand*. Some clocks also have a thin short arm known as the second hand.

The dial of the clock is a circle.( Yes.. yes.. it means the total number of degrees on a clock is 360°.) The circumference of the dial is divided into 12 parts, called* hour spaces. *Each hour space is divided into 5 parts called as *minute spaces. *Thus the whole circumference of dial is divided into 12 × 5 = 60 minute spaces.

I know, now you might be wondering about the angle covered by the hour hand and minute hand for various time intervals. Here is the table giving its details.

**Some facts about clocks: **

- Did you know? During every hour, minute hand and hour hand coincides once. i.e the angle between these two hands is 0°.
- Thus, in 24 hours, the two hands coincided with each other 24 times!!
- Both hands coincide after every 720/11 mins. That means, approximately, after every 65 minutes, the two hands coincide!!!

**Some important types of clock problems:**

Type 1) What is the angle between the minute hand and hour hand of a clock at any given time?

Type 2) What is the time when the angle between minute hand and hour hand is given?

Type 3) What is the time gap between two instants when angle between minute hand and hour hand is given?

**Formula to find angle between the hour hand and minute hand:**

Angle between H hrs and M mins = |60H – 11M| / 2

where H is the hour reading and M is the minute reading for the given time.

**To find mirror image of given time:**

Type 1) Time between 11 and 1: Substract the given value from 23:60

Type 2) Any time (except the time between 11 and 1): Substract the given value from 11:60

Watch out this space for more practice problems and CSIR NET exam solutions on clock problems.

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